Answer:
(a) 35 heads correspond to -3 on the standard scale.
(b) z = 2.4 corresponds to 62 heads on the number of heads scale.
Step-by-step explanation:
(a) If we flip a fair coin once, probability of getting head = 0.5
If we flip a fair coin 100 times, mean number of heads = 100(0.5) = 50
If there are N draws with a P probability of success, the standard deviation (SD) is given as:
![SD = \sqrt{(N)(P)(1 - P)}](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7B%28N%29%28P%29%281%20-%20P%29%7D)
Here, the probability of getting a head (P) is 0.5 while the number of draws (N) is 100. So,
![SD = \sqrt{(100)(0.5)(1-0.5)}](https://tex.z-dn.net/?f=SD%20%3D%20%5Csqrt%7B%28100%29%280.5%29%281-0.5%29%7D)
SD = 5
The standard scale value is: (35 - 50) / 5 = -3
Hence, 35 heads correspond to -3 on the standard scale.
(b) The standard scale value is 2.4 and we need to find the number of heads.
(X - 50) / 5 = 2.4
X - 50 = 12
X = 62
Hence, z = 2.4 on the standard scale corresponds to 62 on the number of heads scale.